Question: Solve for $x$ and $y$ using elimination. ${2x+6y = 42}$ ${-2x+5y = 2}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $11y = 44$ $\dfrac{11y}{{11}} = \dfrac{44}{{11}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {2x+6y = 42}\thinspace$ to find $x$ ${2x + 6}{(4)}{= 42}$ $2x+24 = 42$ $2x+24{-24} = 42{-24}$ $2x = 18$ $\dfrac{2x}{{2}} = \dfrac{18}{{2}}$ ${x = 9}$ You can also plug ${y = 4}$ into $\thinspace {-2x+5y = 2}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(4)}{= 2}$ ${x = 9}$